Solve (64x^3/27)^2/3

$$( \frac { 64 x ^ { 3 } } { 27 } ) ^ { 2 / 3 }$$

Evaluate

$$\frac{16x^{2}}{9}$$

Solution Steps

To raise \frac{64x^{3}}{27} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(64x^{3}\right)^{\frac{2}{3}}}{27^{\frac{2}{3}}}$$

Expand \left(64x^{3}\right)^{\frac{2}{3}}.

$$\frac{64^{\frac{2}{3}}\left(x^{3}\right)^{\frac{2}{3}}}{27^{\frac{2}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{2}{3} to get 2.

$$\frac{64^{\frac{2}{3}}x^{2}}{27^{\frac{2}{3}}}$$

Calculate 64 to the power of \frac{2}{3} and get 16.

$$\frac{16x^{2}}{27^{\frac{2}{3}}}$$

Calculate 27 to the power of \frac{2}{3} and get 9.

$$\frac{16x^{2}}{9}$$

Differentiate w.r.t. x

$$\frac{32x}{9}$$